Apparatus and method for generating and using a pilot signal

ABSTRACT

A method and apparatus is for generating a modulation signal that comprises a resource block. A resource element sequence, M n   p , of M pilot symbols is determined that corresponds to an n th  of N subcarriers. A pilot frequency domain sample sequence, r n   p , corresponding to the resource element sequence M n   p  comprises a quantity, R n   NZ , of non-zero magnitude pilot frequency domain samples. R n   NZ  is determined based on M and an excess bandwidth, α, of an adjacent subcarrier filter. The resource element sequence M n   p , which has no inter-subcarrier interference, is multiplexed with N−1 resource element sequences to form the resource block. The modulation signal is generated by modulating each subcarrier of the N subcarriers with a corresponding resource element sequence of the N resource element sequences and filtering each of the modulated subcarriers using a subcarrier filter. The resource element sequence M n   p  is used during receiving for efficiently determining a channel estimate.

FIELD OF THE INVENTION

The present invention relates generally to data transmission andreception, and more specifically to the use of a pilot signal to providechannel estimation at a receiver.

BACKGROUND

Pilot signals (or reference signals) are commonly used in datatransmissions to allow a receiver to make an estimate of characteristicsof a radio channel in which the data is transmitted, allowing improvedreception accuracy. For the proposed version of transmission schemeknown as Generalized Frequency Division Multiplexing (GFDM), two pilotschemes have been discussed, a preamble technique and a scattered pilotsymbol technique with interference pre-cancellation. The preambletechnique is based on adding pilot symbols (time division multiplexedsymbols that occupy all subcarriers or a significant portion of thecarrier bandwidth) as a preamble to a modulated data block. Thescattered pilot symbol technique adds pilot symbols (frequency divisionmultiplexed) within a multiplexed data block. Each technique has certainadvantages and drawbacks. In particular, the preamble technique allowsreuse of known preamble techniques but has the possibility of higheroverhead and out of band emissions. The scattered pilot symbol withinterference pre-cancellation may provide fairly efficient overhead butmay incur a power penalty and additional hardware for high dynamic rangebetween subcarriers. Furthermore, the use of this scheme for multipleantennas is unclear.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying figures, where like reference numerals refer toidentical or functionally similar elements throughout the separateviews, together with the detailed description below, are incorporated inand form part of the specification, and serve to further illustrateembodiments of concepts that include the claimed invention, and explainvarious principles and advantages of those embodiments. The descriptionis meant to be taken in conjunction with the accompanying drawings inwhich:

FIG. 1 is a functional block diagram that shows a transmitter section ofan electronic device, in accordance with certain embodiments.

FIG. 2 is a functional block diagram that shows a receiver section of anelectronic device, in accordance with certain embodiments.

FIG. 3 is a hardware block diagram that shows a portion of an electronicdevice, in accordance with certain embodiments.

FIG. 4 is a hardware block diagram that shows a portion of an electronicdevice, in accordance with certain embodiments.

FIG. 5 is a time-frequency representation of one example of a smallresource block, in accordance with certain embodiments.

FIG. 6 is a frequency plot that shows subcarrier filter gaincharacteristics and digital sample magnitudes at discrete samplingpoints of a modulated resource block, in accordance with an embodiment.

FIG. 7 is a frequency plot that shows subcarrier filter gaincharacteristics and digital sample magnitudes at discrete samplingpoints of a modulated resource block that has been generated using adiscrete Fourier transform, in accordance with some embodiments.

FIG. 8 is a flow chart that shows some steps of a method for generatinga modulation signal, in accordance with some embodiments.

FIGS. 9-15 are flow charts that show some additional steps that may beperformed in the method described with reference to FIG. 8, inaccordance with some embodiments.

FIG. 16 is a flow chart that shows some additional steps of the methodfor generating a modulation signal described with reference to FIG. 15,in accordance with some embodiments.

FIG. 17 is a flow chart shows some steps that may be used in the methodfor generating a modulation signal described above with reference toFIG. 8, in accordance with some embodiments.

FIG. 18 is a flow chart that shows some additional steps of the methodfor generating a modulation signal described with reference to FIG. 17,in accordance with some embodiments.

FIG. 19 is a flow chart that shows some steps of a method for receivinga carrier demodulated RF signal, in accordance with some embodiments.

Skilled artisans will appreciate that elements in the figures areillustrated for simplicity and clarity and have not necessarily beendrawn to scale. For example, the dimensions of some of the elements inthe figures may be exaggerated relative to other elements to help toimprove understanding of the embodiments.

DETAILED DESCRIPTION

In the description below, like reference numerals are used to describethe same, similar or corresponding parts in the several views of thedrawings. Numerous specific details are set forth to provide a fullunderstanding of the subject technology. It will be obvious, however, toone ordinarily skilled in the art that the subject technology may bepracticed without some of these specific details. In other instances,well-known structures and techniques have not been shown in detail so asnot to obscure the subject technology.

Embodiments described herein generally relate to generating and usingpilot symbols within Generalized Frequency Division Multiplexing (GFDM)protocols, which may include Cyclic Prefix Orthogonal Frequency DivisionMultiplexing (CP-OFDM) and Single Carrier Frequency DivisionMultiplexing (SC-FDM protocols). Certain embodiments describe using oneor more subcarriers exclusively for pilot symbols, wherein the pilotsymbols are designed to avoid inter-subcarrier interference.

Referring to FIG. 1, a functional block diagram 100 shows a transmittersection 110 of an electronic device 105, in accordance with certainembodiments. The electronic device 105 may a transmitter only device,such as, for one example, a cellular base station transmitter. Anotherexample would be a low power sensor, such as a medical or environmentalmonitor. The electronic device 105 may be an electronic device that hasan associated transmitter, such as any type of personal two waycommunication device, including but not limited to cellular telephones,tables, and computers. The electronic device 105 may be operating at anyradio carrier frequency. The transmitter section 110 comprises aresource block modulator 120 that accepts as an input a series of datasymbols 115, each of which may be complex values (just one example ofsuch complex valued symbols are symbols that are 16-QAM (quadratureamplitude modulated)). The resource block modulator 120 determinesvalues 116 which characterize resource blocks currently being formedfrom the series of data symbols 115. Using the values 116, the resourceblock modulator 120 generates one or more data symbol sequences anddetermines one or more pilot symbol sequences (or reference symbolsequences) from stored data or by calculation. The pilot symbolsequences are formed in accordance with unique techniques described morefully below that render them largely free from inter-subcarrierinterference. The data symbol sequences and pilot symbol sequences areused by the resource block modulator 120 to form modulated resourceblocks 121. A resource element sequence is one of either a data symbolsequence or a pilot symbol sequence.

The values 116 may include two integer values, M and N, which define,respectively, a quantity of resource element time slots (or symbol-blocklength) and a quantity of subcarriers of the resource blocks currentlybeing formed, as well as information (such as a base subcarrierfrequency and subcarrier separation or subcarrier spacing) thatdetermines characteristics of subcarrier frequencies, as well assubcarrier filter characteristics. The values 116 that characterize theresource blocks that are being formed and the pilot symbol sequences maybe determined from values stored persistently within the electronicdevice 105, such as in a table, or that are stored transiently by theelectronic device 105, such as data received by the electronic device105 in a control message. Each of the one or more pilot symbol sequencesis associated with a different one of the N subcarriers. These may betermed pilot subcarriers. The subcarriers in general are typicallyarranged as adjacent subcarriers, but pilot subcarriers are typicallynon-adjacent to other pilot subcarriers. The data symbols may representa wide variety of types of information, such as audio (music, voice,etc.), video (camera images, TV, etc.) and telemetry (environmentalsensors, radar results, etc.).

Each resource block is then used to generate one of the modulatedresource blocks of signal 121, as follows. Each resource elementsequence (pilot or data symbol sequence) of a resource block isseparately pulse shaped with a filter {tilde over (g)}[n] where {tildeover (g)}[n] is a circular filter with a period M×N. The time period foreach symbol is a reciprocal of the subcarrier frequency spacing. Aresulting symbol block can be written as follows:

$\begin{matrix}{{x\lbrack k\rbrack} = {\sum\limits_{i = 0}^{M - 1}\; {\sum\limits_{n = 0}^{N - 1}{{d_{n}\lbrack i\rbrack}{\overset{\sim}{g}\left\lbrack {k - {iN}} \right\rbrack}^{{j2\pi}\frac{nk}{N}}}}}} & (1)\end{matrix}$

In equation (1), k is the index that identifies modulated resourceelement samples, n is the index that identifies specific subcarriers,and i is the index for time slots (each time slot has the time period ofa symbol). More than one pilot symbol sequence may be included in eachresource block, at intervals that have been determined to be at most theminimum needed such that radio channel characteristics determined forthe pilot subcarriers provide sufficiently accurate representations ofthe radio channel characteristics of the one or more subcarrierscomprising data symbols. A cyclical prefix is added to form a completemodulated resource block of signal 121. The coherence time of the radiochannel (i.e., the time duration over which the radio channel is assumedto be sufficiently constant) is assumed typically to be at least thesymbol-block length (M time periods) such that the radio channel can beassumed to be almost constant over the symbol-block. Subcarriers with noassociated symbol sequence are not modulated and are considered as nullsubcarriers. The modulated resource block of signal 121 is coupled to anRF modulator 125, which mixes it with carrier reference 122, which maybe a quadrature reference signal. The resulting modulated RF carriersignal 126 is coupled to an RF power amplifier 130. The resultingamplified modulated RF carrier signal is coupled to an antenna 135 andradiated. An RF final stage comprises the RF modulator 125, the RF poweramplifier 130, and the antenna 135.

In some embodiments, such as Multiple Input, Multiple Output (MIMO)embodiments, modulated resource blocks in signal 121 are generated forsimultaneous transmission using the same RF carrier frequency. The pilotsymbol sequences in each resource block intended for simultaneoustransmission are determined in a manner described below that renderspilot symbol sequences of equivalent subcarriers in the differentresource blocks (intended for simultaneous transmission) as orthogonalor largely orthogonal. The data symbol sequences and possibly the pilotsymbol sequences of the two or more resource blocks in signal 121intended for simultaneous transmission may be precoded, for example, byapplying a precoding matrix. The two or more resource blocks in signal121 intended for simultaneous transmission are modulated and themodulated signals are coupled to RF modulators 145 (not shown in FIG. 1)and amplifiers 150 (not shown in FIG. 1) to generate simultaneousmodulated RF signals that are amplified and coupled to additionalantennas (not shown in FIG. 1) for transmission. The multiple modulatedRF signals may comprise identical data symbols or differing datasymbols, depending on system configuration (e.g., diversity versusspatial division multiplexing). In MIMO embodiments or singletransmitter embodiments, one antenna may be used for both transmissionand interception by including a duplexer per receive-transmit signalpair, as is known in the art.

Referring to FIG. 2, a functional block diagram 200 shows a receiversection 210 of an electronic device 205, in accordance with certainembodiments. The electronic device 205 may a receiver only device, suchas, for one example, a cellular base station receiver. Another examplecould be an alert device. The electronic device 205 may be an electronicdevice that has an associated transmitter, such as any type of personaltwo way communication device, including but not limited to cellulartelephones, tables, and computers. The electronic device 205 may beoperating at any radio carrier frequency. The receiver section 210comprises an antenna 215 that intercepts RF energy and converts it to anRF signal 216 that is coupled to an RF amplifier 220 (e.g., a low noiseRF amplifier). The RF signal 216 is amplified by the RF amplifier 220,generating an amplified RF signal 221 that is coupled to an RFdemodulator 225. The RF demodulator uses a carrier signal 227 (which maybe a quadrature signal) to demodulate the amplified RF signal 221,generating an RF demodulated signal 226 that includes sequentialmodulated resource blocks. The modulated resource blocks are such asthose described above with reference to FIG. 1, but they have beenaltered by radio channel characteristics, inter-subcarrier interference,and noise.

The RF demodulated signal 226 is coupled to a channel estimator 230 andto a symbol recovery function 235. The channel estimator 230 and symbolrecovery function 235 determine values 231 which characterize themodulated resource blocks currently being received by the receiversection 205. The values 231 may include the same information describedabove with reference to FIG. 1 and values 116. Using the values 231, thechannel estimator 230 determines from stored data or by calculation oneor more known pilot symbol sequences that are expected to be in eachresource block. The channel estimator 230 uses the known pilot symbolsequences to determine one or more channel estimates 232 from the RFdemodulated signal 226 corresponding to the one or more known pilotsequences in each sequential resource block. The pilot symbol sequencesare pilot symbol sequences that have been determined in accordance withunique techniques described with reference to FIGS. 1 and FIGS. 8-18.The pilot symbol sequences that are being used may be determined frompersistent memory within the electronic device 205, such as in a table,by using the values 231. The values 231 may be received in a controlsignal or may be determined from persistent memory within the electronicdevice, such as another table, using protocol identification received ina control signal. Alternatively, the pilot symbol sequences may begenerated by the channel estimator function 230 or the data symbolrecovery function 235 based on the values 231.

The symbol recovery function 235 uses the values 231 to characterize theresource blocks being received. The symbol recovery function 235recovers the sequences of data symbols 236 from each sequential resourceblock using the characterization of the resource blocks (from the values231) being received and the channel estimates made by the channelestimator 230 for each pilot sequence. This is done by an iterativeprocess that removes adjacent subcarrier interference between adjacentdata symbol modulated subcarriers, without having to re-calculatechannel estimates made from the pilot symbol modulated subcarriers,because inter-subcarrier interference is avoided for pilot symbols, asdescribed below. The recovered data symbols 236 may represent a widevariety of types of information, such as described above with referenceto data symbol types in FIG. 1. In some embodiments, such as MultipleInput, Multiple Output (MIMO) embodiments, one or more modulated RFsignals are simultaneously received from multiple antennas. The multiplemodulated RF signals may comprise identical data symbols or differingdata symbols, depending on the protocol (e.g., diversity receptionversus spatial division reception). In these MIMO embodiments, thechannel estimator uses the values 231 and the RF demodulated signals 226to make channel estimates 232 for each pilot sequence in eachsimultaneously received resource block. The symbol recovery function 230then recovers the data symbols 236 for each resource block of the MIMOtransmission. Interference between pilot symbol sequences insimultaneously transmitted and received RF signals is avoided orminimized by techniques described below. In MIMO embodiments or singletransmitter embodiments, one antenna may be used for both transmissionand interception by included a duplexer per receive-transmit signalpair, as is known in the art.

Referring to FIG. 3, a hardware block diagram 300 shows a portion of anelectronic device 305, in accordance with certain embodiments. Theelectronic device 305 may be any of those described above with referenceto FIG. 1. The portion of the electronic device 305 comprises aprocessing system 325, a digital-to-analog (D/A) converter 330, andamong other things, receives the series of data symbols 115, receivesthe values 116, and generates a modulated resource block in signal 121as described with reference to FIG. 1. The processing system 325comprises a processing function 310 and memory 315. The processingfunction 310 comprises one or more processing devices (only one is shownin FIG. 3), each of which may include such sub-functions as centralprocessing units (cores), cache memory, instruction decoders, just toname a few. The processing function 310 executes program instructionswhich may be located within memory in the processing devices or may belocated in a memory 315 external to the processing function 310, towhich the memory 315 is bi-directionally coupled, or in a combination ofboth. The memory 315 may be any combination of hardware that storesprogramming instructions, such as RAM, ROM, EPROM, EEPROM, and parts ofan ASIC. The processing function 310 may, in some embodiments, becoupled to the D/A convertor 320 as a separate device, and is typicallycoupled to other functions of the electronic device not shown in FIG. 3.

The hardware block diagram 300 (FIG. 3) shows the executable operatinginstructions (EOI) 316 being stored in the memory 315, external to theprocessing function 310, but as noted above, the memory 315 may bewithin or shared with the one or more processing devices. The memory 315also stores data 394. The EOI 316 of the electronic device 305 includesgroups of instructions identified as an operating system (OS) 390,software applications 392 (including software utilities), and a softwareapplication called the resource block modulator 393. The applications392 may include conventional radio applications and may include humaninterface applications. Examples of conventional radio applicationsinclude standby applications and radio control applications. Examples ofhuman interface applications include display and keyboard applications,game applications, navigation application, video processingapplications, and sensor processing applications. In some embodiments,the human interface applications are executed in a separate processingsystem. The processing function 310 includes input/output (I/O)interface circuitry (not explicitly shown) that is controlled by theprocessing function 310. The I/O circuitry is coupled to the signal 115conveying the series of data symbols and may be coupled to thedigital-to-analog (D/A) convertor 330 by signal 326. In someembodiments, the D/A convertor 330 is a portion of the processingfunction 310.

The processing system 325 runs the resource block modulation application393, which performs the functions of the resource block modulator 120(FIG. 1) of electronic device 105 (FIG. 1), except D/A conversion when aseparate D/A convertor 330 is used. A first embodiment of the resourceblock modulator 120 comprises that portion of the processing system 325necessary to perform the functions of the resource block modulator 120,and specifically includes the operating instructions of the resourceblock modulation application 393. A second embodiment of the resourceblock modulator 120 comprises the D/A convertor 330 and that portion ofthe processing system necessary to perform the remaining functions ofthe resource block modulator 120, and specifically includes theoperating instructions of the resource block modulation application 393.

Referring to FIG. 4, a hardware block diagram 400 shows a portion of anelectronic device 405, in accordance with certain embodiments. Theelectronic device 405 may be any of those described above with referenceto FIG. 2. The portion of the electronic device 405 comprises aprocessing system 425, an analog-to-digital (A/D) converter 430, andamong other things, receives a RF demodulated signal as signal 226,receives values 231, and generates recovered data symbols 236 asdescribed with reference to FIG. 2. The processing system 425 comprisesa processing function 410 and memory 415. The processing function 410comprises one or more processing devices (only one is shown in FIG. 4),each of which may include such sub-functions as central processing units(cores), cache memory, instruction decoders, just to name a few. Theprocessing function 410 executes program instructions which may belocated within memory in the processing devices or may be located in amemory 415 external to the processing function 410, to which the memory415 is bi-directionally coupled, or in a combination of both. The memory415 may be any combination of hardware that stores programminginstructions, such as RAM, ROM, EPROM, EEPROM, and parts of an ASIC. Theprocessing function 410 may, in some embodiments, be coupled to the A/Dconvertor 420, and is typically coupled to other functions of theelectronic device not shown in FIG. 4.

The hardware block diagram 400 (FIG. 4) shows the executable operatinginstructions (EOI) 416 being stored in the memory 415, external to theprocessing function 410, but as noted above, the memory 415 may bewithin or shared with the one or more processing devices. The memory 415also stores data 494. The EOI 416 of the electronic device 405 includesgroups of instructions identified as an operating system (OS) 490,software applications 492 (including software utilities), and a softwareapplication called the receiving application 493. The receivingapplication 493 comprises two sub-applications, a channel estimatorapplication and a symbol recovery application. The applications 492 mayinclude conventional radio applications and may include human interfaceapplications. Examples of conventional radio applications includestandby applications and radio control applications. Examples of humaninterface applications include display and keyboard applications, gameapplications, navigation application, video processing applications, andsensor processing applications. In some embodiments, the human interfaceapplications are executed in a separate processing system. Theprocessing function 410 includes input/output (I/O) interface circuitry(not explicitly shown) that is controlled by the processing function410. The I/O circuitry is coupled to the RF demodulated signal 226 andmay be coupled to the A/D convertor 430 by signal 426. In someembodiments, the A/D convertor 430 is a portion of the processingfunction 410.

The processing system 425 runs the receiving application 493, whichperforms the functions of the channel estimator function 230 (FIG. 2)and symbol recovery function 235 (FIG. 2) of electronic device 205 (FIG.2), except A/D conversion when a separate D/A convertor 430 is used. Afirst embodiment of the channel estimator function 230 and symbolrecovery function 235 comprises that portion of the processing system425 necessary to perform the functions of the channel estimator function230 and symbol recovery function 235, and specifically includes theoperating instructions of the receiving application 493. A secondembodiment of the resource block modulator 120 comprises the A/Dconvertor 430 and that portion of the processing system necessary toperform the remaining functions of the channel estimator function 230and symbol recovery function 235, and specifically includes theoperating instructions of the receiving application 493.

Referring to FIG. 5, a time-frequency representation 500 of one exampleof a small resource block 505 is shown, in accordance with certainembodiments. The small resource block 505 shown in FIG. 5 has foursubcarriers 510. The number of subcarriers 510 is identified as N inthis document. In this example, N=4. The number of time slots 515 orsymbol-block length in this document is indicated by M. In this example,M=5. Each resource element may be a pilot symbol or a data symbol. A setof multicarrier resource elements modulated on the N subcarriers istransmitted simultaneously in each time slot. Resource elements that aredata symbols are designated as d_(n) (i), whereas resource elements thatare pilot symbols are designated as d_(n) ^(p) (i). In thesedesignations, 0≦n<N and 0≦i<M. Resource element 520, d₃ (3), isspecifically referenced in FIG. 5 as an example. In theserepresentations, p indicates a pilot symbol, n indicates a specificsubcarrier, and the i within d_(n) (i) indicates a specific time slot. Alack of superscript indicates a data symbol. In the time period at theleft of the representation, a block CP is identified. This is arepresentation of a cyclic prefix in the time domain of a certainduration (e.g., typically a fraction of the time slot duration) thatprecedes the M time slots or symbol-block in the time domain and is areplica of the samples at the end of symbol-block of duration equal tothe cyclic prefix duration. In this small resource block 505 there isonly one pilot sequence on one pilot subcarrier. The inclusion of onepilot sequence on one pilot subcarrier may be used in circumstances inwhich a channel estimate made by a receiver using the pilot symbols ofthe one pilot sequence on the pilot subcarrier is expected tocharacterize the channel for subcarriers 0, 2, and 3 sufficiently wellto allow adequate recovery of all the data symbols in the resource block505. This expectation may be based on several characteristics of theenvironment in which the resource block is transmitted, for example, theRF carrier frequency, the RF bandwidth (which is typically closelyrelated to the sum of the bandwidths of the subcarriers), the nature ofmultipath in the RF channel, the filter characteristics of thesubcarrier filters, etc. In large resource blocks, a multiplicity ofpilot symbol sequences or pilot subcarriers may be used. In someembodiments, location or position of the pilot subcarrier(s) ondifferent resource blocks may be different. In some embodiments,location or position of pilot subcarrier(s) of a resource block of afirst symbol-block may be different than the location or position ofpilot subcarrier(s) of the resource block of a second symbol-block. Thelocation or position of pilot subcarrier(s) may be determined by apredetermined hopping sequence which may be based on an Identity of anelectronic device or an Identity signaled by an electronic device.

Referring to FIG. 6, a frequency plot 605 shows subcarrier filter gaincharacteristics and digital sample magnitudes at discrete samplingpoints of a modulated resource block that has been generated using aDiscrete Fourier Transform, in accordance with an embodiment. The gainaxis 610 shows subcarrier filter gains normalized to a maximum valueof 1. The frequency axis 615 shows frequencies normalized to a frequencyequal to one subcarrier bandwidth or subcarrier spacing. This embodimentis presented to show problems solved with other embodiments describedbelow. In this example, the N and M values for the resource block arethe same as described with reference to FIG. 5, i.e., N=4 and M=5. Forclarity and simplicity, in this example all data and pilot frequencydomain samples are assumed to have had a magnitude of 1 prior tomodulation and filtering. The subcarrier filters have gaincharacteristics 620-623 in this example and are identical for allsubcarriers, are circular filters, and are root-raised cosine filters(with excess bandwidth factor or rolloff factor α=0.3), which providespulse shaping approximately as shown in FIG. 6, and use an upconversionfactor of two. The filter having gain characteristic 620 is a filter for5 filtered frequency domain samples 635-639 of the 10 upconvertedfiltered frequency domain samples r₀ (i), 0≦i<10 of a data resourceelement sequence, d₀ (i), 0≦i<5. The filter having gain characteristic621 is a filter for the 10 upconverted filtered frequency domain samples650-659, r₁ ^(p) (i), 0≦i<10, of a pilot resource element sequence, d₁^(p) (i), 0≦i<5. The filter having gain characteristic 622 is a filterfor 5 filtered frequency domain samples 670-674 of the 10 upconvertedfiltered frequency domain samples r₂ (i), 0≦i<10 of a data resourceelement sequence, d₂ (i), 0≦i<5. Five filtered sample values for thefirst and third subcarrier resource element sequences and all filtereddata samples for the fourth subcarrier resource element sequence are notshown, for simplicity and clarity.

It will be appreciated that the sample values generated as signal 326(FIG. 3) are combined values that are the weighted sum of the values ofthe filtered symbols occurring from subcarriers at a same sample time.The frequency domain representation of the signal 326 comprises samplesthat are combined values of the sum of the values of the filteredsamples occurring from adjacent subcarrier. For some frequency-domainsamples, the combined value is equal to the value of only one of the twofiltered samples because the other filtered sample has a value of zerodue to filtering. However, there are regions of excess bandwidth, α,which is a measure of excess bandwidth of the subcarrier filter, ofwhich two excess bandwidth regions 690, 691 are shown in FIG. 6. Theexcess bandwidth regions 690, 691 are the regions of a filter gaincharacteristic beyond the Nyquist bandwidth of half symbol rate (i.e.,half subcarrier spacing) to a frequency at which the gain reaches zeroor an insignificant value. In the present case of adjacent subcarrierfilters, the subcarrier filters are arranged such that the Nyquistbandwidth edges of two adjacent filters are at a boundary frequency. Theexcess bandwidth of a filter is quantified herein as a fraction, α, ofthe excess bandwidth of the filter to the Nyquist bandwidth. It will beappreciated that the total value of a sample that falls within thisexcess bandwidth region is the sum of the filtered sample values fromtwo resource element sequences; for example, one being a data symbolsequence on subcarrier n=0 and the other (subcarrier n=1) being a pilotsymbol sequence. This overlap between the adjacent subcarrier filterscontributes to the amounts of inter-subcarrier interference between thedata symbol sequence and pilot symbol sequence.

If this set of transmitted sample values were received by a receiver,the receiver would be attempting to recover a pilot symbol sequence thathas interference from data symbol sequence(s) from adjacentsubcarrier(s). This makes the process of reception complex, because aniterative process must be used to derive a first pass estimate of thechannel characteristics using samples of the received pilot symbolsequence and the known pilot symbol sequence on the pilot subcarrier,which gives an incorrect estimate of the channel characteristics becauseof the interference, in addition to the noise. The incorrect estimatedchannel characteristic may then be used to recover the data symbolsequence(s) that are interfering with the pilot symbol sequence. Therecovered data symbol sequence may be incorrect due to the incorrectchannel estimate and noise. The recovered data symbol sequence may thenbe used to remove the data subcarrier interference from the pilotsubcarrier using the known subcarrier filter characteristics. Thisimproves the quality of the received pilot symbol sequence and in turnimproves the channel estimate which is based on the improved(interference-reduced) pilot symbol sequence. This process may beiterated as much as needed to achieve a desired pilot symbol sequencequality, but the resulting data symbol error rate may still be higherthan desired and the recovery of the channel estimate is complicated andtherefore resource consuming.

In some embodiments a general expression for the signal 121 (FIG. 1) fora pilot sample sequence r_(n) ^(p) (i) for subcarrier n∈{1, . . . ,N} isgiven in equation (2), which is derived from a Discrete FourierTransform of equation (1):

r _(n) ^(p)(i)=(P ^((n−1))Γ_(Tx) ^((L)) R ^((L)) W _(M) d _(n−1) +p^((n))Γ_(Tx) ^((L)) R ^((L)) W _(M) d _(n) +p ^((n+1))Γ_(Tx) ^((L)) R^((L)) W _(M) d _(n+1))   (2)

In equation (2) i={nM+l}, l∈{−M, M−1}, R^((L))={I_(M), I_(M), . . . ,I_(M)}^(T),

${W_{\upsilon} = {\frac{1}{\sqrt{\upsilon}}\left\{ w^{n,m} \right\} \upsilon \times \upsilon}},{W^{n,m} = ^{{- {j2\pi}}\frac{{({n - 1})}{({m - 1})}}{\gamma}}},$

Γ^((L))=W_(LMg) ^((L)), I_(M) is an Identity matrix of size M, L is theupconversion factor (in our example L=2), W_(υ), is a DFT-matrix of sizeυ, g^((L)) is the down-sampled (by factor N/L) version of the filtercoefficient g, and p^((n)) is a permutation matrix for up-converting then^(th) sub-carrier to its respective sub-carrier frequency. Thecoherence time of the channel is preferably at least the resourcesymbol-block length such that the channel can be assumed to be constantover the symbol-block. From this equation, it can be seen that the tensamples for each subcarrier are a sum of values related to thesubcarrier and adjacent subcarriers. In FIG. 6, the values 639, 640,670, 671, which are samples for the adjacent channels, haveinsignificant magnitudes due to filtering, so in this embodiment thereare four sample times at which non-zero values would be added togetherby equation (2) to get the sample values that occur in signal 326. Thesample pairs that are added together at these four sample times are(637, 652), (638, 653), (657, 672), and (658, 673).

Referring to FIG. 7, a frequency plot 705 shows subcarrier filter gaincharacteristics and digital sample magnitudes at discrete samplingpoints of a modulated resource block that has been generated using aDiscrete Fourier Transform, in accordance with some embodiments. Thegain axis 610 and frequency axis 615 are the same as in FIG. 6. In thisexample, the subcarrier filters are identical to those described withreference to FIG. 6. The N and M values for the resource block are thesame as described with reference to FIG. 5, i.e., N=4 and M=5. Forclarity and simplicity, in this example all non-zero magnitude data andpilot frequency domain samples are shown as if they had magnitude of 1.This is not the actual situation, as will be made clear below. Asignificant difference between these embodiments and the embodimentdescribed with reference to FIG. 6 is that the only pilot frequencydomain samples having non-zero values before filtering are determinedsuch that they are in the region 792 of the pilot subcarrier filter gaincharacteristic 621 that is between the defined minimum thresholds of theexcess bandwidths 690, 691 of the adjacent subcarrier filters. In theexample being used, the pilot sample sequence r_(n) ^(p), (n=1) hasnon-zero magnitude samples only for pilot samples r_(n) ^(p)(1), 4≦i ≦6, identified in FIG. 7 as pilot samples 754. 755, 756. All other pilotsamples, r_(n) ^(p)(1), 0≦i ≦3 and r_(n) ^(p)(1), 7≦i≦9, which areidentified in FIGS. 7 as 750, 751, 752, 753 and 757, 758, 759, have zeromagnitude prior to filtering. The filtered sample values of the datasamples in the adjacent subcarriers have the same values as shown inFIG. 6. As a result of the constraint that the only pilot frequencydomain samples having non-zero values before filtering are not withinthe excess bandwidth regions, it will be appreciated that the pilot timedomain symbol sequence incurs no interference from adjacent subcarrierdata or pilot symbol sequence in the same resource block. Thisconstraint may be achieved in some embodiments as described in thefollowing techniques.

Referring to FIG. 8, a flow chart 800 of some steps of a method forgenerating a modulation signal is shown, in accordance with someembodiments. The modulation signal is one such as signal 121 (FIG. 1),generated by an electronic device such as electronic device 105 (FIG.1). At step 805, a quantity, N, of subcarriers that are to be used fortransmitting a first resource block and a quantity, M, of resourceelements corresponding to each subcarrier of the first resource blockare determined. The first resource block comprises the N subcarriers andM multicarrier symbols, and can be used to modulate a radio frequency(RF) carrier. In this context, “first” simply serves to distinguish oneresource block from another, not to identify a relative time ofoccurrence of the resource block. A multicarrier symbol comprises Nsymbols of the same time slot (one or more of which may be pilotsymbols). A first resource element sequence, M_(n) ^(p), of M pilotsymbols is determined at step 810 in the first resource block thatcorresponds to an n^(th) of the N subcarriers. A pilot frequency domainsample sequence, r_(n) ^(p), corresponding to the resource elementsequence M_(n) ^(p) comprises a quantity, R_(n) ^(NZ), of non-zeromagnitude pilot frequency domain samples. R_(n) ^(NZ) is determinedbased on M and an excess bandwidth, α, of an adjacent subcarrier filter.The adjacent subcarrier filter is one that is used to filter a modulatedsubcarrier that is adjacent to the n^(th) subcarrier within the firstresource block. The first resource element sequence M_(n) ^(p)ismultiplexed at step 815 with the N−1 resource element sequences thatcorrespond to the N−1 subcarriers that are not the n^(th) subcarrier, toform the first resource block. At step 820 a first modulation signal isgenerated by modulating each subcarrier of the N subcarriers with acorresponding resource element sequence of the N resource elementsequences. This generates N modulated subcarriers. Each of the Nmodulated subcarriers is filtered using a corresponding one of Nsubcarrier filters, wherein the N subcarrier filters include theadjacent subcarrier filter. In some embodiments, a second resource blockis modulated with a different multi-carrier transmission scheme (e.g.,OFDM of SC-FDM). In some embodiments, one or more guard (or null)subcarriers may be introduced between adjacent resource blocks. This mayhelp to reduce the interference between adjacent resource blocks. Insome embodiments, the guard (or null) subcarriers may be created bysetting the value of the resource element sequence of an edge subcarrierof one or more resource blocks to zero or null. In some embodiments, afirst device is allocated a first set of contiguous resource blocks anda second device is allocated a second set of contiguous resource blocksadjacent to the first set of contiguous resource blocks, and one or moreguard (or null) subcarriers are introduced at the boundary between thefirst set of contiguous resource blocks and second set of contiguousresource blocks. The guard (or null) subcarriers may be edge subcarriercorresponding to the boundary resource block(s) of the first device andsecond device resource allocation.

The R_(n) ^(NZ) non-zero magnitude pilot frequency domain samples maynot be within any excess bandwidth region of the subcarrier and areequally spaced about the center of the bandwidth of the subcarrier. TheR_(n) ^(NZ) non-zero magnitude pilot frequency domain samples arecontiguous in frequency. The values of the time domain pilot signalcorresponding to the n^(th) subcarrier of the first modulation areindependent of the values of data symbols in adjacent subcarriers.

The time domain pilot symbols are symbols for which the R_(n) ^(NZ)non-zero magnitude pilot frequency domain samples meet the statedconstraints (the number of non-zero pilot frequency domain samples isdetermined based on combinations of M and α). The time domain pilotsymbols may be obtained by first forming the complete pilot frequencydomain sample sequence r_(n) ^(p) by zero padding the R_(n) ^(NZ)non-zero magnitude pilot frequency domain samples by a quantity R_(n)^(z)of zero magnitude pilot frequency domain samples. In an example inwhich the subcarrier filter span is characterized over two subcarrierspans corresponding to an upconversion factor of two, R_(n)^(z)=2·M−R_(n) ^(NZ). The zero padded pilot sample sequence may then betransformed by an inverse Discrete Fourier Transform, which may beperformed in some embodiments as an Inverse Fast Frequency Transform, togenerate the pilot symbol sequence, M_(n) ^(p). In some embodiments thisprocess to determine the time domain pilot symbols may be carried outduring a design phase for all expected combinations of M, N, and α atthe time of design of a protocol and the results stored as a look uptable. The determination of the pilot symbols may then be accomplishedin an electronic device 105 by determining a set of M and α values for aparticular transmission, and using the look up table to determine thepilot symbols. The pilot symbols may then be used to perform themultiplex operation to assemble all the symbols for a resource block.This technique provides a common procedure to prepare the modulationsignal 121. This is an efficient process for generating resource blocksthat have pilot sequences that have reduced or no inter-subcarrierinterference. In contrast, it will be appreciated that the modulatedvalues of signal 121 within any subcarrier that is not a pilotsubcarrier is dependent on resource element sequence values (such assymbol values) in adjacent subcarriers (if any) that are not pilotsubcarriers, due to the subcarrier filters. Alternatively, theelectronic device may determine the pilot symbol sequence by making adetermination of the values of M and α, and determining the value R_(n)^(NZ) therefrom using any method, such as a graphical method or any oneof several techniques described herein, to establish values for each ofthe R_(n) ^(NZ) samples, such as heuristically or by any one of severaltechniques described herein below, and performing an Inverse DiscreteFourier Transform to generate the pilot symbols.

In some embodiments, the subcarrier filters have identical gain andbandwidth characteristics. In some embodiments, the filters areroot-raised cosine filter (for example with excess bandwidth factor, orroll-off factor α=0.3). In some embodiments, the filter characteristics,including excess bandwidth, and the values of M and N are determined bythe selection of a particular protocol, which may be influenced byinformation from a network controlling device and/or informationdetermined by the electronic device. For example, the type of data to becommunicated influences the values M and N. The bandwidth resources thatare available for a particular session or message may influence thenumber of subcarriers, N, and may influence the subcarrier bandwidth andsubcarrier filter characteristics. The value of M may be based on theamount of data that is in a particular message or data packet. Thecomplete time domain signal (signal 121, FIG. 1) is the summation of allpilot (and data) signals on the different subcarriers. The summation istypically performed in the discrete time domain, so that signal 326,FIG. 3, may also be considered to the summation of the time domainsignals.

Referring to FIG. 9, a flow chart 900 shows a step of the method thatmay be used in the method for generating a modulation signal that isdescribed above with reference to FIG. 8, in accordance with someembodiments. At step 905, filtering each of the N modulated subcarriers(step 820, FIG. 8) comprises circularly filtering each modulatedsubcarrier using the corresponding one of the N subcarrier filters.

Referring to FIG. 10, a flow chart 1000 shows a step of the method thatmay be used in the method for generating a modulation signal that isdescribed above with reference to FIG. 8, in accordance with someembodiments. In embodiments in which all subcarrier filters areidentical and the subcarrier filters are characterized over twosubcarrier spans, R_(n) ^(NZ) may be determined (step 810, FIG. 8) as

$R_{n}^{NZ} = {{2\left( {M - 1 - \left\lfloor {\frac{M}{2}\left( {1 + \alpha} \right)} \right\rfloor} \right)} + 1.}$

For embodiments in which the subcarrier filters do not have equivalentexcess bandwidths for the two adjacent subcarrier filters, the formulawould be based on the values for α for the subcarrier filters (i.e.,subcarrier filter for subcarrier of interest, and adjacent subcarrierfilters). In one example in which M=5 and α=0.3, R_(n) ^(NZ)=3.

Referring to FIG. 11, a flow chart 1100 shows a step of the method thatmay be used in the method for generating a modulation that is describedabove with reference to FIG. 8, in accordance with some embodiments. Atstep 1105, the pilot frequency domain sequence r_(n) ^(p) is formed thatcomprises the R_(n) ^(NZ) non-zero magnitude pilot frequency domainsamples mapped as contiguous frequency samples corresponding to thefrequency samples close to the center of the pilot subcarrier and aquantity, R_(n) ^(Z), of zero magnitude pilot frequency domain samplesthat is determined based on a subcarrier filter rolloff factor and M. Amethod of determining R_(n) ^(Z) is described above with reference toFIG. 8. The frequency samples encompassing the center frequency sampleof the pilot subcarrier may comprise equally spaced frequency samplesthat in some embodiments with an odd number of frequency samples haveequal number of frequency samples on both upper and lower frequencyportions around the center frequency sample and in other embodimentswith an even number of frequency samples have unequal number offrequency samples (difference of one sample) on the upper and lowerfrequency portions around the center frequency sample of the pilotsubcarrier. The zero magnitude frequency samples may be distributedequally or unequally (e.g., difference of one sample) outside of thenon-zero magnitude frequency samples.

Referring to FIG. 12, a flow chart 1200 shows some steps that may beused in step 810 of the method for generating a modulation signaldescribed above with reference to FIG. 8, in accordance with someembodiments. At step 1205, the R_(n) ^(NZ) non-zero magnitude pilotfrequency domain samples are determined based on a Zadoff-Chu sequenceof length L and base u. A Zadoff-Chu sequence, x_(u)(m), of length L andbase u can be given as,

${{x_{u}(m)} = {\exp\left( {{- {{j\pi}u}}\frac{m\left( {m + 1} \right)}{L}} \right)}},$

m=0,1,2, . . . ,L−1 (1≦u≦L−1). At optional step 1210, in someembodiments, L=R_(n) ^(NZ) and base u is relatively prime with respectto L. In some embodiments, the Zadoff-Chu sequences are determined usinga base that is relatively prime with reference to R_(n) ^(NZ). At step1215, the Zadoff-Chu sequence in some embodiments has a length less thanR_(n) ^(NZ) (e.g., the Zadoff-Chu sequence length L is given by thelargest prime number such that L<R_(n) ^(Nz)) and the R_(n) ^(NZ)non-zero magnitude pilot frequency domain samples are a cyclic extensionof the Zadoff-Chu sequence, x_(u)(n mod L), 0≦n<R_(n) ^(Nz). At step1220, in some embodiments the Zadoff-Chu sequence has a length more thanR_(n) ^(Nz) (e.g., the Zadoff-Chu sequence length L is given by thesmallest prime number such that L>R_(n) ^(Nz)) and the R_(n) ^(Nz)non-zero magnitude pilot frequency domain samples are a truncation ofthe Zadoff-Chu sequence (x_(u)(n), 0≦n<R_(n) ^(Nz)). It will beappreciated that the Inverse Discrete Fourier Transform of a Zadoff-Chusequence of length L results in a sequence of time symbols of constantamplitude, and for which cyclical shifts of the pilot time symbols orpilot frequency domain samples are orthogonal, respectively, to othershifts. Cyclic extension and truncation somewhat degrades these aspects.Zadoff-Chu is alternatively designated ZC in this document.

In some embodiments, the R_(n) ^(Nz) non-zero magnitude pilot frequencydomain samples are determined based on a pre-determined QPSK (QuadraturePhase Shift Keying) modulation sequence. In some embodiments, the R_(n)^(Nz) non-zero magnitude pilot frequency domain samples are scrambled bya pseudo-random scrambling sequence. The pseudo-random scramblingsequence may be based on an Identity of an electronic device or anIdentity signaled by an electronic device. The pseudo-random scramblingsequence may be a complex scrambling sequence such as a QPSK scramblingsequence with in-phase and quadrature-phase sequences based on a realvalued pseudo-random sequence, for example, determined from aPseudoNoise (PN) sequence or Gold sequence generator.

One consequence of forming pilot symbol sequences with the type ofshaping of the pilot signal in frequency domain describe herein (i.e.,the quantity of non-zero frequency domain samples R_(q) ^(Nz) is lessthan M) for a smaller number of non-zero frequency domain samples thanM, is that it is possible that the signals on different time slots(d^(p) (i), 0≦i≦M−1) have different powers. For instance, for a selectedfrequency response of a length-5 symbol-block (M=5) for which R_(q)^(Nz)=3, wherein a first value for the base u of a Zadoff-Chu sequenceis used, a scaled r_(u) ^(p)(n)=(1.291, −0.645−1.118i, 1.291). In thetime domain, d^(p)(n)=(0.8660−0.5000i, 0.2388+0.4446i, −0.8534+1.0085i,0.0976−1.3175i, −0.3490+0.3645i). So, the corresponding power of eachtime slot of the length-5 symbol-block would be (1, 0.504, 1.32, 1.32,0.504). As can be seen, although the total power (in time) is the sameas the power that exists for data subcarriers, it is not constant overdifferent time-slots. To reduce or remove this time dependency whenmultiple pilot signals are used (e.g., in a resource block, or acrossresource blocks) an appropriate phase shift may be applied to the r_(u)^(p)(n) such that for different pilot subcarriers a time-shifted versionof the time-domain representation of the original pilot signal aregenerated, i.e.:

d _(n) ^(p)=η×

_(u) ^((β,n))(1:2:2M)   (³)

In equation (3), η is a normalization factor to compensate for thezero-padding in the frequency domain, and

_(u) ^((β,n))(n)=IFFT (e^(−jnk)r_(u) ^(p)(n)) with a cyclic shift of β.For instance, as for the above example, equation (3) gives the followingpilot sequences:

d ₁ ^(p)=Seq1=(0.86−0.50i, 0.23+0.44i, −0.85+1.00i, 0.09−1.31i,−0.34+0.36i)

d ₂ ^(p)=Seq2=(−0.34+0.36i, 0.86−0.50i, 0.23+0.44i, −0.85+1.00i,0.09−1.31i)

d ₃ ^(p)=Seq3=(0.09−1.31i, −0.34+0.36i, 0.86−0.50i, 0.23+0.44i,−0.85+1.00i)

d ₄ ^(p)=Seq4=(−0.85+1.00i, 0.09−1.31i, −0.34+0.36i, 0.86−0.50i,0.23+0.44i)

d ₅ ^(p)=Seq5=(0.23+0.44i, −0.85+1.00i, 0.09−1.31i, −0.34+0.36i,0.86−0.50 i)

d ₆ ^(p)=Seq6=(0.86−0.50i, 0.23+0.44i, −0.85+1.00i, 0.09−1.31i, −0.34+0.36i)=d ₁ ^(p)

Seq7=one shift to the right of Seq6

Seq8=so on . . .

With this time shift and since the complete time domain signal is thesummation of all pilot (and data) signals on different subcarriers, theaverage power over different timeslots would be almost equal to eachother and large power variations will not occur between time samples ofthe symbol-block. Some steps for achieving this are described withreference to FIGS. 13-14.

Referring to FIG. 13, a flow chart 1300 shows some steps that may beused in the method for generating a modulation signal that is describedabove with reference to FIG. 8, in accordance with some embodiments. Atstep 1305, a second resource element sequence, M_(q) ^(p:θS), of M pilotsymbols that form a q^(th) of the N subcarriers is determined, whereinq≠n, and wherein pilot frequency domain samples, r_(q) ^(p)(i), 0<i<M−1,of the q^(th) subcarrier corresponding to the second resource elementsequence M_(q) ^(p:θS) are each determined as at least a phase shift,θ(i), of the corresponding pilot frequency domain samples, r_(n)^(p)(i), 0<i<M−1, of the n^(th) subcarrier, and wherein θ(i)=Q·i, andwherein Q is a phase constant. The phrase “at least” is used becauseother techniques that are described below could be combined with thisone to alter the values of the pilot symbols of the first resourceelement sequence. The second resource element sequence M_(q) ^(p:θS) ismultiplexed, at step 1310, with the N−1 resource element sequences thatcorrespond to the N−1 subcarriers that are not the q^(th) subcarrier, toform the first resource block. (Note that the first resource elementsequence M_(n) ^(p) has already been multiplexed in step 815 describedabove with reference to FIG. 8). The phrase “at least” is used becauseother techniques that are described below could be combined with phaseshifting to obtain the values of the pilot symbols of the secondresource element sequence. It will be appreciated that using one or moreversions of a pilot frequency domain samples sequence (for example byapplying a phase shift) typically reduces the amount of amplitudevariation of the modulated resource block signal.

Referring to FIG. 14, a flow chart 1400 shows some steps that may beused in the method for generating a modulation signal that is describedabove with reference to FIG. 8, in accordance with some embodiments. Atstep 1405, a second resource element sequence, M_(q) ^(p:TS) of M pilotsymbols that form the resource elements for a q^(th) one of the Nsubcarriers of the first resource block is determined, wherein q≠n, andwherein the pilot symbols, d_(q) ^(p)(i), 0<i<M−1, of the q^(th)subcarrier are each determined as a cyclical time shift of the pilotsymbols, d_(n) ^(p)(i), 0<i<M−1, of the n^(th) subcarrier. At step 1410,the second resource element sequence M_(q) ^(p:TS) is multiplexed withthe N−1 resource element sequences that correspond to the N−1subcarriers that are not the q^(th) subcarrier, to form the firstresource block. (Note that the first resource element sequence M_(n)^(p) has already been multiplexed in step 815 described above withreference to FIG. 8). It will be appreciated that these embodiments areequivalent to the embodiments described above with reference to FIG. 13,when an appropriate phase shift constant Q is chosen.

Referring to FIG. 15, a flow chart 1500 shows some steps that may beused in the method for generating a modulation signal that is describedabove with reference to FIG. 8, in accordance with some embodiments. Atstep 1505, a second resource element sequence, M_(q) ^(p:CS), of M pilotsymbols that correspond to a q^(th) of N subcarriers of a secondresource block is determined. The subcarriers and subcarrier filters ofthe second resource block may have the same characteristics of thesubcarriers and subcarrier filters used for the first resource block.The pilot subcarrier, q, of the second resource block may be the same asthe pilot subcarrier, n, used for the first resource block. A pilotfrequency domain samples sequence, r_(q) ^(p:CS), corresponding to thesecond resource element sequence M_(q) ^(p:CS), comprises R_(q) ^(NZ)non-zero magnitude pilot frequency domain samples. R_(q) ^(NZ)=R_(n)^(NZ). The R_(q) ^(NZ) non-zero magnitude pilot frequency domain samplesof the pilot frequency domain samples sequence r_(q) ^(p:CS) of thesecond resource block are determined as cyclical shifts of therespective R_(n) ^(NZ) non-zero magnitude pilot frequency domain samplesof the pilot frequency domain samples sequence r_(n) ^(p)of the firstresource block. Note that q may be any value from 0 to N−1, including n.At step 1510, the second resource element sequence M_(q) ^(p:CS) ismultiplexed with the N−1 resource element sequences that correspond tothe N−1 subcarriers that are not the q^(th) subcarrier, to form thesecond resource block. At step 1515, a second modulation signal isgenerated by modulating each subcarrier with a corresponding resourceelement sequence of the second resource block, which generates Nmodulated subcarriers of the second resource block, and filtering eachof the N modulated subcarriers of the second resource block using acorresponding one of N subcarrier filters. It will be appreciated thatthis technique can be extended to more than two resource elementsequences of M pilot symbols.

Referring to FIG. 16, a flow chart 1600 shows some additional steps ofthe method for generating a modulation signal described above withreference to FIG. 15, in accordance with some embodiments. At step 1605,a first RF carrier is modulated with the first modulation signal togenerate a first modulated RF signal. The first modulated RF signal iscoupled to a first antenna port. At step 1610, a second RF carrier withthe second modulation signal to generate a second modulated RF signal.The second modulated RF signal is coupled to a second antenna port,wherein the second antenna port is different than the first antennaport. The first and second modulation RF signals may be transmittedsimultaneously, in synchronism. An “antenna port” according to certainembodiments may be a logical port that may correspond to a beam(resulting from beam forming) or may correspond to a physical antenna atan electronic device. An antenna port can be defined such that thechannel over which a symbol on the antenna port is conveyed can beinferred from the channel over which another symbol on the same antennaport is conveyed. In some embodiments, a physical antenna may mapdirectly to a single antenna port, in which case an antenna portcorresponds to an actual physical antenna. Alternately, a set or subsetof physical antennas, or antenna set, may be mapped to one or moreantenna ports after applying complex weights, a cyclic delay, or both tothe signal on each physical antenna. The physical antenna set may haveantennas from a single electronic device or from multiple electronicdevices. The weights may be fixed as in an antenna virtualizationscheme, such as cyclic delay diversity (CDD). The pilot signalsassociated with an antenna port may be specific or common to alldestination devices. The procedure used to derive antenna ports fromphysical antennas may be specific to an electronic device implementationand transparent to other electronic devices. In accordance with someembodiments, the first antenna port and the second antenna port may bequasi-located such that the large-scale properties of the channel overwhich a symbol on first antenna port is conveyed can be inferred fromthe channel over which a symbol on the second antenna port is conveyed.The large-scale properties can include one or more of delay spread,Doppler spread, Doppler shift, average gain, and average delay.

Referring to FIG. 17, a flow chart 1700 shows some steps that may beused in the method for generating a modulation signal described abovewith reference to FIG. 8, in accordance with some embodiments. At step1705, a second resource element sequence, M_(q) ^(p:U), of M pilotsymbols that correspond to a q^(th) of N subcarriers of a secondresource block is determined. The pilot subcarrier, q, of the secondresource block may be the same as the pilot subcarrier, n, used for thefirst resource block. A pilot frequency domain samples sequence, r_(q)^(p:U), corresponding to the second resource element sequence M_(q)^(p:U), comprises R_(q) ^(NZ) non-zero magnitude values. R_(q)^(NZ)=R_(n) ^(NZ). The R_(n) ^(NZ) non-zero magnitude pilot frequencydomain samples of the pilot frequency domain samples sequence r_(n)^(p)) are based on a first Zadoff-Chu sequence having a first base. TheR_(q) ^(NZ) non-zero magnitude pilot frequency domain samples of thepilot frequency domain samples sequence r_(q) ^(p:U) are based on asecond Zadoff-Chu sequence having a second base, preferably of the samelength as the first ZC sequence. Note that q may be any value from 0 toN−1, including n, and the first base is different than the second base.At step 1710, the second resource element sequence M_(q) ^(p:U) ismultiplexed with the N−1 resource element sequences that correspond tothe N−1 subcarriers that are not the q^(th) subcarrier to form thesecond resource block. At step 1715, a second modulation signal isgenerated by modulating each subcarrier with a corresponding resourceelement sequence of the second resource block, which generates Nmodulated subcarriers, and filtering each of the N modulated subcarriersusing a corresponding one of N subcarrier filters.

Referring to FIG. 18, a flow chart 1800 shows some additional steps ofthe method for generating a modulation signal described above withreference to FIG. 17, in accordance with some embodiments. At step 1805,a first RF carrier is modulated with the first modulation signal togenerate a first modulated RF signal. The first modulated RF signal iscoupled to a first antenna port. At step 1810, a second RF carrier withthe second modulation signal to generate a second modulated RF signal.The second modulated RF signal is coupled to a second antenna port,wherein the second antenna port is different than the first antennaport.

Zadoff-Chu sequences keep their constant amplitude and correlationproperty after FFT and IFFT operations, meaning that if they areorthogonal in one domain they will be orthogonal in other domain aswell. Another important point is that, due to the way that the ZCsequences are generated, the effective length of the sequences areR^(NZ) not M. Therefore at most R^(NZ) different cyclic shifts of theZadoff-Chu sequence can be used to generate fully orthogonal Zadoff-Chupilot signals. Different bases of the same Zadoff-Chu sequence lengthmay be also be used to achieve a high degree of quasi-orthogonality (lowcross-correlation) in some embodiments. It is this property that isdescribed with reference to FIGS. 17 and 18. In cases in which differentbase ZC sequences are used, these sequences are not completelyorthogonal but have a correlation of

$\frac{1}{\sqrt{R^{NZ}}}$

which may be sufficiently small in long resource blocks to provide adesired accuracy of signal recovery in a receiver. Note that for smallresource block lengths,

$\frac{1}{\sqrt{R^{NZ}}}$

will not be a small number and application of Zadoff-Chu sequences withdifferent bases may result in high interference and inaccurate channelestimation).

Benefits of embodiments described herein with reference to FIGS. 15-18are that they can support simultaneous transmission of multipleorthogonal pilots (either in a multiple antenna case or in a case ofinter-cell coordination transmissions from multiple cellular basestations for reducing the interference over pilot signals). To multiplexdifferent pilots the property of the Zadoff-Chu sequences is used thatZadoff-Chu sequences of the same length and base are orthogonal to eachother if they have different cyclic shift offset values, i.e.,Zadoff-Chu sequences of any length have an “ideal” periodicautocorrelation (i.e., the correlation with the circularly shiftedversion of itself is a delta function).

The techniques described herein above as described with reference toFIGS. 13-18, may be used in combination. As an example, in a resourceblock of length 5 symbol-block (M=5) with α=0.3, there may be threeinterference-free samples. So, for up to 3 pilot signals a multiplexingof three Zadoff-Chu sequences (different cyclic shift values) with thesame base u can be used: r_(u) ⁽⁰⁾(k) (no cyclic shift), r_(u) ⁽¹⁾(k)(cyclic shift value of 1), and r_(u) ⁽²⁾(k) (cyclic shift value of 2),where gcd(u, 3)=1, i.e., u=1 or 2. If more pilot symbol sequences areneeded, ZC sequences can be added with base u_(n)≠u_(q), wherein thegcd(u_(q),3)=1. Using both cyclic shifting and ZC sequences of the samelength and different bases is a combination of techniques described withreference to FIGS. 15-18 that may be used in a signal transmitted on oneantenna port or two or more signals formulated to simultaneouslytransmit resource blocks including different data symbols on differentantenna ports. Also, the techniques with reference to FIGS. 13-14 ofapplying a phase shift to the pilot frequency domain samples or cyclictime shift to the pilot symbols on different pilot subcarriers of signaltransmitted from a given antenna can be combined with the techniqueswith reference to FIGS. 15-18 of multiple orthogonal pilots signalgeneration for simultaneous transmission from different antenna ports toreduce the power variations of signals across the time slots or betweensymbols of a symbol-block from each antenna port of the differentantenna ports.

Referring to FIG. 19, a flow chart 1900 shows some steps of a method forreceiving a carrier demodulated RF signal, in accordance with someembodiments. At step 1905, a subcarrier that includes known pilotsymbols within a resource block of the carrier demodulated RF isidentified, wherein the known pilot symbols are formed to be free frominter-subcarrier interference. At step 1910, synchronization isperformed to a clock of the carrier demodulated RF signal. At step 1915,a channel estimate based on carrier demodulated RF signal and the knownpilot symbols is determined. At step 1920, inter-subcarrier interferencebetween at least two subcarriers of data symbols is removed iterativelywithout determining a new channel estimate.

The iteration in step 1920 comprises, in some embodiments, a firstestimate of the data symbols on the data subcarriers in the resourceblock is determined using the channel estimate assuming nointer-subcarrier interference between two adjacent subcarriers. Thisfirst estimate of data symbols forms the latest or most recent estimateof the data symbol estimate for the iterative (one or iteration)interference canceller. On an iteration of the interference canceller,for a data subcarrier, inter-subcarrier interference from at least oneadjacent subcarrier of the data subcarrier is estimated based on themost recent estimate of the data symbol sequence on the at least oneadjacent subcarrier, the subcarrier filter, and other characteristics ofthe resource block modulator. The estimated inter-subcarrierinterference is subtracted from the carrier demodulated RF signal, andthe data symbol sequence on the data subcarrier is re-estimated andbecomes the most recent estimate of the data symbol sequence on the datasubcarrier. This process (estimation of the inter-subcarrierinterference on a data subcarrier, subtracting the estimate, andre-estimating the data symbol sequence on the data subcarrier resultingin the most recent estimate the data symbol sequence on the datasubcarrier) is repeated for each data subcarrier (preferablysequentially in data subcarrier index) in the resource block using thelatest or most recent estimate of the data symbol sequences on theadjacent subcarriers to estimate the inter-subcarrier interference onthe data subcarrier. Once the data symbols on all the data subcarriersof the resource block are re-estimated, a next iteration of theinterference canceller can be performed. The number of iterations maycontinue until a convergence criteria is met (e.g., packet issuccessfully decoded) or a maximum iteration limit is reached. In someembodiments, interference cancellation begins with the data subcarrieradjacent to the pilot subcarrier and sequentially proceeds to the otherdata subcarriers away from the pilot subcarrier.

It will be appreciated that an electronic device such as some of thosedescribed with reference to FIG. 1 can perform the methods describedwith reference to FIGS. 8-18.

It will be appreciated that an electronic device such as those describedwith reference to FIG. 2 can perform the methods described withreference to FIG. 19.

It should be apparent to those of ordinary skill in the art that for themethods described herein other steps may be added or existing steps maybe removed, modified or rearranged without departing from the scope ofthe methods. Also, the methods are described with respect to theapparatuses described herein by way of example and not limitation, andthe methods may be used in other systems.

In this document, relational terms such as first and second, top andbottom, and the like may be used solely to distinguish one entity oraction from another entity or action without necessarily requiring orimplying any actual such relationship or order between such entities oractions. The terms “comprises,” “comprising,” or any other variationthereof, are intended to cover a non-exclusive inclusion, such that aprocess, method, article, or apparatus that comprises a list of elementsdoes not include only those elements but may include other elements notexpressly listed or inherent to such process, method, article, orapparatus. An element preceded by “comprises . . . a” does not, withoutmore constraints, preclude the existence of additional identicalelements in the process, method, article, or apparatus that comprisesthe element. The term “coupled” as used herein is defined as connected,although not necessarily directly and not necessarily mechanically.

Reference throughout this document are made to “one embodiment”,“certain embodiments”, “an embodiment” or similar terms The appearancesof such phrases or in various places throughout this specification arenot necessarily all referring to the same embodiment. Furthermore, theparticular features, structures, or characteristics attributed to any ofthe embodiments referred to herein may be combined in any suitablemanner in one or more embodiments without limitation.

The term “or” as used herein is to be interpreted as an inclusive ormeaning any one or any combination. Therefore, “A, B or C” means “any ofthe following: A; B; C; A and B; A and C; B and C; A, B and C”. Anexception to this definition will occur only when a combination ofelements, functions, steps or acts are in some way inherently mutuallyexclusive.

The processes illustrated in this document, for example (but not limitedto) the method steps described in FIGS. 8-19, may be performed usingprogrammed instructions contained on a computer readable medium whichmay be read by processor of a CPU. A computer readable medium may be anytangible medium capable of storing instructions to be performed by amicroprocessor. The medium may be one of or include one or more of a CDdisc, DVD disc, magnetic or optical disc, tape, and silicon basedremovable or non-removable memory. The programming instructions may alsobe carried in the form of packetized or non-packetized wireline orwireless transmission signals.

It will be appreciated that some embodiments may comprise one or moregeneric or specialized processors (or “processing devices”) such asmicroprocessors, digital signal processors, customized processors andfield programmable gate arrays (FPGAs) and unique stored programinstructions (including both software and firmware) that control the oneor more processors to implement, in conjunction with certainnon-processor circuits, some, most, or all of the functions of themethods and/or apparatuses described herein. Alternatively, some, most,or all of these functions could be implemented by a state machine thathas no stored program instructions, or in one or more applicationspecific integrated circuits (ASICs), in which each function or somecombinations of certain of the functions are implemented as customlogic. Of course, a combination of the approaches could be used.

Further, it is expected that one of ordinary skill, notwithstandingpossibly significant effort and many design choices motivated by, forexample, available time, current technology, and economicconsiderations, when guided by the concepts and principles disclosedherein will be readily capable of generating such stored programinstructions and ICs with minimal experimentation.

In the foregoing specification, specific embodiments have beendescribed. However, one of ordinary skill in the art appreciates thatvarious modifications and changes can be made without departing from thescope of the present invention as set forth in the claims below.Accordingly, the specification and figures are to be regarded in anillustrative rather than a restrictive sense, and all such modificationsare intended to be included within the scope of present invention. Thebenefits, advantages, solutions to problems, and any element(s) that maycause any benefit, advantage, or solution to occur or become morepronounced are not to be construed as a critical, required, or essentialfeatures or elements of any or all the claims. The invention is definedsolely by the appended claims including any amendments made during thependency of this application and all equivalents of those claims asissued.

What is claimed is:
 1. A method for generating a modulation signal,comprising: determining a quantity, N, of subcarriers that are to beused for transmitting a first resource block and a quantity, M, ofresource elements corresponding to each subcarrier of the first resourceblock, wherein the first resource block comprises the N subcarriers andM multicarrier symbols and can be used to modulate a radio frequency(RF) carrier; determining a first resource element sequence, M_(n) ^(p),of M pilot symbols in the first resource block that corresponds to ann^(th) of the N subcarriers, wherein a pilot frequency domain samplessequence, r_(n) ^(p), corresponding to the resource element sequenceM_(n) ^(p), comprises a quantity, R_(n) ^(NZ), of non-zero magnitudepilot frequency domain samples, wherein R_(n) ^(NZ) is determined basedon M and an excess bandwidth, α, of an adjacent subcarrier filter;multiplexing the first resource element sequence M_(n) ^(p)with the N−1resource element sequences that correspond to the N−1 subcarriers thatare not the n^(th) subcarrier, to form the first resource block; andgenerating a first modulation signal by modulating each of the Nsubcarriers with a corresponding resource element sequence of the Nresource element sequences, which generates N modulated subcarriers, andfiltering each of the N modulated subcarriers using a corresponding oneof N subcarrier filters, wherein the N subcarrier filters include theadjacent subcarrier filter.
 2. The method according to claim 1, whereinfiltering each of the N modulated subcarriers comprises circularlyfiltering each modulated subcarrier using the corresponding one of the Nsubcarrier filters.
 3. The method according to claim 1, where in theR_(n) ^(NZ) non-zero magnitude pilot frequency domain samples may not bewithin any excess bandwidth region of the subcarrier and are equallyspaced about the center of the bandwidth of the subcarrier.
 4. Themethod according to claim 1, wherein values of a pilot signalcorresponding to the n^(th) subcarrier of the first modulation signal inthe first resource block are independent of the values of symbols inresource element sequences of any adjacent subcarrier.
 5. The methodaccording to claim 1, further comprising: determining R_(n) ^(NZ) as$R_{n}^{NZ} = {{2\left( {M - 1 - \left\lfloor {\frac{M}{2}\left( {1 + \alpha} \right)} \right\rfloor} \right)} + 1.}$6. The method according to claim 1, further comprising: forming thepilot frequency domain sequence r_(n) ^(p) that comprises the R_(n)^(NZ) non-zero magnitude pilot frequency domain samples mapped ascontiguous frequency samples corresponding to the frequency samplesclose to the center of the pilot subcarrier and a quantity, R_(n) ^(Z),of zero magnitude pilot frequency domain samples that is determinedbased on a subcarrier filter roll-off factor and M.
 7. The methodaccording to claim 1, further comprising: determining the R^(NZ)non-zero magnitude pilot frequency domain samples based on a Zadoff-Chusequence.
 8. The method according to claim 7, wherein the Zadoff-Chusequence has a length R^(NZ).
 9. The method according to claim 7,wherein the Zadoff-Chu sequence has a length less than R^(NZ) and theR^(NZ) non-zero magnitude pilot frequency domain samples are a cyclicextension of the Zadoff-Chu sequence.
 10. The method according to claim7, wherein the Zadoff-Chu sequence has a length more than R^(NZ) and theR^(NZ) non-zero magnitude pilot frequency domain samples are atruncation of the Zadoff-Chu sequence.
 11. The method according to claim1, further comprising: determining a second resource element sequence,M_(q) ^(p:θS), of M pilot symbols that form a q^(th) of the Nsubcarriers, wherein q≠n, and wherein pilot frequency domain samples,r_(q) ^(p)(i), of the q^(th) subcarrier corresponding to the secondresource element sequence M_(q) ^(p:θS) are each determined as at leasta phase shift, θ(i), of the corresponding pilot frequency domainsamples, r_(n) ^(p)(i) , of the n^(th) subcarrier, and wherein θ(i)=Q·i,and wherein Q is a phase constant; and multiplexing the second resourceelement sequence M_(q) ^(p:θS) with the N−1 resource element sequencesthat correspond to the N−1 subcarriers that are not the q^(th)subcarrier to form the first resource block.
 12. The method according toclaim 1, further comprising: determining a second resource elementsequence, M_(q) ^(p:TS), of M pilot symbols that form the resourceelements for a q^(th) one of the N subcarriers of the first resourceblock, wherein q≠n, and wherein the pilot symbols, d_(q) ^(p)(i),0<i<M−1, of the q^(th) subcarrier are each determined as a cyclical timeshift of the pilot symbols, d_(n) ^(p)(i) , 0<i<M−1, of the n^(th)subcarrier; and multiplexing the second resource element sequence M_(q)^(p:TS) with the N−1 resource element sequences that correspond to theN−1 subcarriers that are not the q^(th) subcarrier, to form the firstresource block.
 13. The method according to claim 1, further comprising:determining a second resource element sequence, M_(q) ^(p:CS), of Mpilot symbols that correspond to a q^(th) of N subcarriers of a secondresource block, wherein a pilot frequency domain samples sequence, r_(q)^(p:U), corresponding to the second resource element sequence, M_(q)^(p:CS), comprises R_(q) ^(NZ) non-zero magnitude pilot frequency domainsamples, and wherein the R_(q) ^(NZ) non-zero magnitude pilot frequencydomain samples of the pilot frequency domain samples sequence r_(q)^(p:U) of the second resource block are determined as a cyclical shiftsof the respective R_(n) ^(NZ) non-zero magnitude pilot frequency domainsamples of the pilot frequency domain samples sequence r_(n) ^(p) of thefirst resource element sequence M_(n) ^(p) of the first resource block;multiplexing the second resource element sequence M_(q) ^(p:CS) with theN−1 resource element sequences that correspond to the N−1 subcarriersthat are not the q^(th) subcarrier, to form the second resource block;and generating a second modulation signal by modulating each subcarrierwith a corresponding resource element sequence of the second resourceblock, which generates N modulated subcarriers of the second resourceblock, and filtering each of the N modulated subcarriers of the secondresource block using a corresponding one of N subcarrier filters. 14.The method according to claim 13, further comprising: modulating a firstRF carrier with the first modulation signal to generate a firstmodulated RF signal and coupling the first modulated RF signal to afirst antenna port; and modulating a second RF carrier with the secondmodulation signal to generate a second modulated RF signal and couplingthe second modulated RF signal to a second antenna port, wherein thesecond antenna port is different than the first antenna port.
 15. Themethod according to claim 1, further comprising: determining a secondresource element sequence, M_(q) ^(p:U), of M pilot symbols thatcorrespond to q^(th) of N subcarriers of a second resource block,wherein a pilot frequency domain samples sequence, r_(q) ^(p:U),corresponding to the second resource element sequence M_(q) ^(p:U),comprises R_(q) ^(NZ) non-zero magnitude values, and wherein the R_(n)^(NZ) non-zero magnitude pilot frequency domain samples of the pilotfrequency domain samples sequence r_(n) ^(p) are based on a firstZadoff-Chu sequence having a first base, and wherein the R_(q) ^(NZ)non-zero magnitude pilot frequency domain samples r_(q) ^(p:U)(i_(NZ))of the pilot frequency domain samples sequence, r_(q) ^(p:U) are basedon a second Zadoff-Chu sequence having a second base, and wherein thefirst base is different than the second base; multiplexing the secondresource element sequence M_(q) ^(U)with the N−1 resource elementsequences that correspond to the N−1 subcarriers that are not the q^(th)subcarrier to form the second resource block; and generating a secondmodulation signal by modulating each subcarrier with a correspondingresource element sequence of the second resource block, which generatesN modulated subcarriers, and filtering each of the N modulatedsubcarriers using a corresponding one of N subcarrier filters.
 16. Themethod according to claim 15, further comprising: modulating a first RFcarrier with the first modulation signal to generate a first modulatedRF signal and coupling the first modulated RF signal to a first antennaport; and modulating a second RF carrier with the second modulationsignal to generate a second modulated RF signal and coupling the secondmodulated RF signal to a second antenna port, wherein the second antennaport is different than the first antenna port.
 17. A method forreceiving a carrier demodulated RF signal, comprising: identifying asubcarrier that includes known pilot symbols within a resource block ofthe carrier demodulated RF signal, wherein the known pilot symbols areformed to be free from inter-subcarrier interference; synchronizing to aclock of the carrier demodulated RF signal; determining a channelestimate based on carrier demodulated RF signal and the known pilotsymbols; and iteratively removing inter-subcarrier interference betweenat least two subcarriers of data symbols without determining a newchannel estimate.
 18. The method for receiving a carrier demodulated RFsignal according to claim 17, wherein the forming of the known pilotsymbols comprises: determining a quantity, N, of subcarriers that are tobe used for transmitting a first resource block and a quantity, M, ofresource elements corresponding to each subcarrier of the first resourceblock, wherein the first resource block comprises the N subcarriers andM multicarrier symbols and can be used to modulate a radio frequency(RF) carrier; determining a first resource element sequence, M_(n) ^(p),of M pilot symbols in the first resource block that corresponds to ann^(th) of the N subcarriers, wherein a pilot frequency domain samplessequence, r_(n) ^(p), corresponding to the resource element sequenceM_(n) ^(p), comprises a quantity, R_(n) ^(NZ), of non-zero magnitudepilot frequency domain samples, wherein R_(n) ^(NZ) is determined basedon M and an excess bandwidth, α, of an adjacent subcarrier filter;multiplexing the first resource element sequence M_(n) ^(p) with the N−1resource element sequences that correspond to the N−1 subcarriers thatare not the n^(th) subcarrier, to form the first resource block; andgenerating a first modulation signal by modulating each of the Nsubcarriers with a corresponding resource element sequence of the Nresource element sequences, which generates N modulated subcarriers, andfiltering each of the N modulated subcarriers using a corresponding oneof N subcarrier filters, wherein the N subcarrier filters include theadjacent subcarrier filter.
 19. An apparatus, comprising: a processingsystem comprising a processor and a memory, wherein the memory includesprogram instructions that control the processor to determine a quantity,N, of subcarriers that are to be used for transmitting a first resourceblock and a quantity, M, of resource elements corresponding to eachsubcarrier of the first resource block, wherein the first resource blockcomprises the N subcarriers and M multicarrier symbols and can be usedto modulate a radio frequency (RF) carrier, determine a first resourceelement sequence, M_(n) ^(p), of M pilot symbols in the first resourceblock that corresponds to an n^(th) of the N subcarriers, wherein apilot frequency domain samples sequence, r_(n) ^(p), corresponding tothe resource element sequence M_(n) ^(p), comprises a quantity, R_(n)^(NZ), of non-zero magnitude pilot frequency domain samples, whereinR_(n) ^(NZ) is determined based on M and an excess bandwidth, α, of anadjacent subcarrier filter, multiplex the first resource elementsequence M_(n) ^(p) with the N−1 resource element sequences thatcorrespond to the N−1 subcarriers that are not the n^(th) subcarrier, toform the first resource block, and generate a first modulation signal bymodulating each of the N subcarriers with a corresponding resourceelement sequence of the N resource element sequences, which generates Nmodulated subcarriers, and filtering each of the N modulated subcarriersusing a corresponding one of N subcarrier filters, wherein the Nsubcarrier filters include the adjacent subcarrier filter; and an RFfinal stage that modulates an RF carrier with the first modulationsignal to generate a modulated RF signal, amplifies the modulated RFsignal to generate an amplified RF signal, and couples the amplified RFsignal to an antenna.
 20. A tangible media comprising programmedinstructions that when executed by a processor performs: determining aquantity, N, of subcarriers that are to be used for transmitting a firstresource block and a quantity, M, of resource elements corresponding toeach subcarrier of the first resource block, wherein the first resourceblock comprises the N subcarriers and M multicarrier symbols and can beused to modulate a radio frequency (RF) carrier; determining a firstresource element sequence, M_(n) ^(p), of M pilot symbols in the firstresource block that corresponds to an n^(th) of the N subcarriers,wherein a pilot frequency domain samples sequence, r_(n) ^(p),corresponding to the resource element sequence M_(n) ^(p), comprises aquantity, R_(n) ^(NZ), of non-zero magnitude pilot frequency domainsamples, wherein R_(n) ^(NZ) is determined based on M and an excessbandwidth, α, of an adjacent subcarrier filter; multiplexing the firstresource element sequence M_(n) ^(p)with the N−1 resource elementsequences that correspond to the N−1 subcarriers that are not the n^(th)subcarrier, to form the first resource block; and generating a firstmodulation signal by modulating each of the N subcarriers with acorresponding resource element sequence of the N resource elementsequences, which generates N modulated subcarriers, and filtering eachof the N modulated subcarriers using a corresponding one of N subcarrierfilters, wherein the N subcarrier filters include the adjacentsubcarrier filter.